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8eb1ebb8d2
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58a5c38e62
@ -1,203 +0,0 @@
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module Viewer
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using Blink
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using Colors
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using Printf
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export ConstructionViewer, display!, opentools!, closetools!
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# === Blink utilities ===
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append_to_head!(w, type, content) = @js w begin
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@var element = document.createElement($type)
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element.appendChild(document.createTextNode($content))
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document.head.appendChild(element)
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end
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style!(w, stylesheet) = append_to_head!(w, "style", stylesheet)
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script!(w, code) = append_to_head!(w, "script", code)
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# === construction viewer ===
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mutable struct ConstructionViewer
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win::Window
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function ConstructionViewer()
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# create window and open developer console
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win = Window(Blink.Dict(:width => 620, :height => 830))
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# set stylesheet
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style!(win, """
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body {
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background-color: #ccc;
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}
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/* the maximum dimensions keep Ganja from blowing up the canvas */
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#view {
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display: block;
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width: 600px;
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height: 600px;
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margin-top: 10px;
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margin-left: 10px;
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border-radius: 10px;
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background-color: #f0f0f0;
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}
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#control-panel {
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width: 600px;
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height: 200px;
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box-sizing: border-box;
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padding: 5px 10px 5px 10px;
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margin-top: 10px;
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margin-left: 10px;
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overflow-y: scroll;
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border-radius: 10px;
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background-color: #f0f0f0;
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}
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#control-panel > div {
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margin-top: 5px;
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padding: 4px;
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border-radius: 5px;
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border: solid;
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font-family: monospace;
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}
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""")
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# load Ganja.js
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loadjs!(win, "https://unpkg.com/ganja.js")
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# create global functions and variables
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script!(win, """
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// create algebra
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var CGA3 = Algebra(4, 1);
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// initialize element list and palette
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var elements = [];
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var palette = [];
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// declare handles for the view and its options
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var view;
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var viewOpt;
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// declare handles for the controls
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var controlPanel;
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var visToggles;
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// create scene function
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function scene() {
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commands = [];
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for (let n = 0; n < elements.length; ++n) {
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if (visToggles[n].checked) {
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commands.push(palette[n], elements[n]);
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}
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}
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return commands;
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}
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function updateView() {
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requestAnimationFrame(view.update.bind(view, scene));
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}
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""")
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@js win begin
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# create view
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viewOpt = Dict(
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:conformal => true,
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:gl => true,
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:devicePixelRatio => window.devicePixelRatio
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)
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view = CGA3.graph(scene, viewOpt)
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view.setAttribute(:id, "view")
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view.removeAttribute(:style)
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document.body.replaceChildren(view)
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# create control panel
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controlPanel = document.createElement(:div)
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controlPanel.setAttribute(:id, "control-panel")
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document.body.appendChild(controlPanel)
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end
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new(win)
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end
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end
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function display!(viewer::ConstructionViewer, elements::Matrix)
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# load elements
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elements_full = [
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[0; elt; fill(0, 26)]
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for elt in eachcol(elements)
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]
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@js viewer.win elements = $elements_full.map((elt) -> @new CGA3(elt))
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# generate palette. this is Gadfly's `default_discrete_colors` palette,
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# available under the MIT license
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palette = distinguishable_colors(
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length(elements_full),
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[LCHab(70, 60, 240)],
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transform = c -> deuteranopic(c, 0.5),
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lchoices = Float64[65, 70, 75, 80],
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cchoices = Float64[0, 50, 60, 70],
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hchoices = range(0, stop=330, length=24)
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)
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palette_packed = [RGB24(c).color for c in palette]
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@js viewer.win palette = $palette_packed
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# create visibility toggles
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@js viewer.win begin
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controlPanel.replaceChildren()
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visToggles = []
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end
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for (elt, c) in zip(eachcol(elements), palette)
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vec_str = join(map(t -> @sprintf("%.3f", t), elt), ", ")
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color_str = "#$(hex(c))"
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style_str = "background-color: $color_str; border-color: $color_str;"
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@js viewer.win begin
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@var toggle = document.createElement(:div)
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toggle.setAttribute(:style, $style_str)
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toggle.checked = true
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toggle.addEventListener(
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"click",
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() -> begin
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toggle.checked = !toggle.checked
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toggle.style.backgroundColor = toggle.checked ? $color_str : "inherit";
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updateView()
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end
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)
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toggle.appendChild(document.createTextNode($vec_str))
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visToggles.push(toggle);
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controlPanel.appendChild(toggle);
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end
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end
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# update view
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@js viewer.win updateView()
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end
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function opentools!(viewer::ConstructionViewer)
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size(viewer.win, 1240, 830)
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opentools(viewer.win)
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end
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function closetools!(viewer::ConstructionViewer)
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closetools(viewer.win)
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size(viewer.win, 620, 830)
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end
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end
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# ~~~ sandbox setup ~~~
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# in the default view, e4 + e5 is the point at infinity
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elements = sqrt(0.5) * BigFloat[
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1 1 -1 -1 0;
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1 -1 1 -1 0;
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1 -1 -1 1 0;
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0 0 0 0 -sqrt(6);
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1 1 1 1 2
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]
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# show construction
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viewer = Viewer.ConstructionViewer()
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Viewer.display!(viewer, elements)
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@ -1,76 +0,0 @@
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<!DOCTYPE html>
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<html>
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<head>
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<style>
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body {
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background-color: #ffe0f0;
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}
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/* needed to keep Ganja canvas from blowing up */
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canvas {
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min-width: 600px;
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max-width: 600px;
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min-height: 600px;
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max-height: 600px;
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}
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</style>
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<script src="https://unpkg.com/ganja.js"></script>
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</head>
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<body>
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<p><button onclick="flip()">Flip</button></p>
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<script>
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// in the default view, e4 + e5 is the point at infinity
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let CGA3 = Algebra(4, 1);
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let elements = [
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CGA3.inline(() => Math.sqrt(0.5)*( 1e1 + 1e2 + 1e3 + 1e5))(),
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CGA3.inline(() => Math.sqrt(0.5)*( 1e1 - 1e2 - 1e3 + 1e5))(),
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CGA3.inline(() => Math.sqrt(0.5)*(-1e1 + 1e2 - 1e3 + 1e5))(),
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CGA3.inline(() => Math.sqrt(0.5)*(-1e1 - 1e2 + 1e3 + 1e5))(),
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CGA3.inline(() => -Math.sqrt(3)*1e4 + Math.sqrt(2)*1e5)()
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];
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// set up palette
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var colorIndex;
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var palette = [0xff00b0, 0x00ffb0, 0x00b0ff, 0x8040ff, 0xc0c0c0];
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function nextColor() {
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colorIndex = (colorIndex + 1) % palette.length;
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return palette[colorIndex];
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}
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function resetColorCycle() {
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colorIndex = palette.length - 1;
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}
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resetColorCycle();
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// create scene function
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function scene() {
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commands = [];
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resetColorCycle();
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elements.forEach((elt) => commands.push(nextColor(), elt));
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return commands;
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}
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// initialize graph
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let graph = CGA3.graph(
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scene,
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{
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conformal: true, gl: true, grid: true
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}
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)
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document.body.appendChild(graph);
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function flip() {
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let last = elements.length - 1;
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for (let n = 0; n < last; ++n) {
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// reflect
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elements[n] = CGA3.Mul(CGA3.Mul(elements[last], elements[n]), elements[last]);
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// de-noise
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for (let k = 6; k < elements[n].length; ++k) {
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elements[n][k] = 0;
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}
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}
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requestAnimationFrame(graph.update.bind(graph, scene));
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}
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</script>
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</body>
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</html>
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@ -1,127 +0,0 @@
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using Blink
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using Colors
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# === utilities ===
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append_to_head!(w, type, content) = @js w begin
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@var element = document.createElement($type)
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element.appendChild(document.createTextNode($content))
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document.head.appendChild(element)
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end
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style!(w, stylesheet) = append_to_head!(w, "style", stylesheet)
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script!(w, code) = append_to_head!(w, "script", code)
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function add_element!(vec)
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# add element
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full_vec = [0; vec; fill(0, 26)]
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n = @js win elements.push(@new CGA3($full_vec))
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# generate palette. this is Gadfly's `default_discrete_colors` palette,
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# available under the MIT license
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palette = distinguishable_colors(
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n,
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[LCHab(70, 60, 240)],
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transform = c -> deuteranopic(c, 0.5),
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lchoices = Float64[65, 70, 75, 80],
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cchoices = Float64[0, 50, 60, 70],
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hchoices = range(0, stop=330, length=24)
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)
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palette_packed = [RGB24(c).color for c in palette]
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@js win palette = $palette_packed
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end
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# === build page ===
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# create window and open developer console
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win = Window()
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opentools(win)
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# set stylesheet
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style!(win, """
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body {
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background-color: #ffe0f0;
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}
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/* needed to keep Ganja canvas from blowing up */
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canvas {
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min-width: 600px;
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max-width: 600px;
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min-height: 600px;
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max-height: 600px;
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}
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""")
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# load Ganja.js
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loadjs!(win, "https://unpkg.com/ganja.js")
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# create global functions and variables
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script!(win, """
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// create algebra
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var CGA3 = Algebra(4, 1);
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// initialize element list and palette
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var elements = [];
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var palette = [];
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// declare visualization handle
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var graph;
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// create scene function
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function scene() {
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commands = [];
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for (let n = 0; n < elements.length; ++n) {
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commands.push(palette[n], elements[n]);
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}
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return commands;
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}
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function flip() {
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let last = elements.length - 1;
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for (let n = 0; n < last; ++n) {
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// reflect
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elements[n] = CGA3.Mul(CGA3.Mul(elements[last], elements[n]), elements[last]);
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// de-noise
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for (let k = 6; k < elements[n].length; ++k) {
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elements[n][k] = 0;
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}
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}
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requestAnimationFrame(graph.update.bind(graph, scene));
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}
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""")
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# set up controls
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body!(win, """
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<p><button id="flip-button" onclick="flip()">Flip</button></p>
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""", async = false)
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# === set up visualization ===
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||||||
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# list elements. in the default view, e4 + e5 is the point at infinity
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elements = sqrt(0.5) * BigFloat[
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1 1 -1 -1 0;
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1 -1 1 -1 0;
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1 -1 -1 1 0;
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0 0 0 0 -sqrt(6);
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1 1 1 1 2
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]
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||||||
# load elements
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for vec in eachcol(elements)
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add_element!(vec)
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||||||
end
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||||||
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||||||
# initialize visualization
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||||||
@js win begin
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||||||
graph = CGA3.graph(
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scene,
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||||||
Dict(
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||||||
"conformal" => true,
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||||||
"gl" => true,
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||||||
"grid" => true
|
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||||||
)
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||||||
)
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||||||
document.body.appendChild(graph)
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||||||
end
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@ -10,10 +10,10 @@ using PolynomialRoots
|
|||||||
# the difference between the matrices `target` and `attempt`, projected onto the
|
# the difference between the matrices `target` and `attempt`, projected onto the
|
||||||
# subspace of matrices whose entries vanish at each empty index of `target`
|
# subspace of matrices whose entries vanish at each empty index of `target`
|
||||||
function proj_diff(target, attempt)
|
function proj_diff(target, attempt)
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||||||
J, K, values = findnz(target)
|
I, J, values = findnz(target)
|
||||||
result = zeros(size(target)...)
|
result = zeros(size(target)...)
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||||||
for (j, k, val) in zip(J, K, values)
|
for (i, j, val) in zip(I, J, values)
|
||||||
result[j, k] = val - attempt[j, k]
|
result[i, j] = val - attempt[i, j]
|
||||||
end
|
end
|
||||||
result
|
result
|
||||||
end
|
end
|
||||||
@ -21,24 +21,24 @@ end
|
|||||||
# === example ===
|
# === example ===
|
||||||
|
|
||||||
# the Lorentz form
|
# the Lorentz form
|
||||||
Q = diagm([1, 1, 1, 1, -1])
|
Q = diagm([-1, 1, 1, 1, 1])
|
||||||
|
|
||||||
# initialize the partial gram matrix for an arrangement of seven spheres in
|
# initialize the partial gram matrix for an arrangement of seven spheres in
|
||||||
# which spheres 1 through 5 are mutually tangent, and spheres 3 through 7 are
|
# which spheres 1 through 5 are mutually tangent, and spheres 3 through 7 are
|
||||||
# also mutually tangent
|
# also mutually tangent
|
||||||
|
I = Int64[]
|
||||||
J = Int64[]
|
J = Int64[]
|
||||||
K = Int64[]
|
|
||||||
values = BigFloat[]
|
values = BigFloat[]
|
||||||
|
for i in 1:7
|
||||||
for j in 1:7
|
for j in 1:7
|
||||||
for k in 1:7
|
if (i <= 5 && j <= 5) || (i >= 3 && j >= 3)
|
||||||
if (j <= 5 && k <= 5) || (j >= 3 && k >= 3)
|
push!(I, i)
|
||||||
push!(J, j)
|
push!(J, j)
|
||||||
push!(K, k)
|
push!(values, i == j ? 1 : -1)
|
||||||
push!(values, j == k ? 1 : -1)
|
|
||||||
end
|
end
|
||||||
end
|
end
|
||||||
end
|
end
|
||||||
gram = sparse(J, K, values)
|
gram = sparse(I, J, values)
|
||||||
|
|
||||||
# set the independent variable
|
# set the independent variable
|
||||||
#
|
#
|
||||||
@ -54,11 +54,11 @@ gram[1, 6] = gram[6, 1]
|
|||||||
# in this initial guess, the mutual tangency condition is satisfied for spheres
|
# in this initial guess, the mutual tangency condition is satisfied for spheres
|
||||||
# 1 through 5
|
# 1 through 5
|
||||||
guess = sqrt(0.5) * BigFloat[
|
guess = sqrt(0.5) * BigFloat[
|
||||||
|
1 1 1 1 2 0.2 0.1;
|
||||||
|
0 0 0 0 -sqrt(6) 0.3 -0.2;
|
||||||
1 1 -1 -1 0 -0.1 0.3;
|
1 1 -1 -1 0 -0.1 0.3;
|
||||||
1 -1 1 -1 0 -0.5 0.4;
|
1 -1 1 -1 0 -0.5 0.4;
|
||||||
1 -1 -1 1 0 0.1 -0.2;
|
1 -1 -1 1 0 0.1 -0.2
|
||||||
0 0 0 0 -sqrt(6) 0.3 -0.2;
|
|
||||||
1 1 1 1 2 0.2 0.1;
|
|
||||||
]
|
]
|
||||||
|
|
||||||
# search parameters
|
# search parameters
|
||||||
@ -108,11 +108,11 @@ println("\nLoss: ", loss, "\n")
|
|||||||
|
|
||||||
# === algebraic check ===
|
# === algebraic check ===
|
||||||
|
|
||||||
R, gens = polynomial_ring(AbstractAlgebra.Rationals{BigInt}(), ["x", "t₁", "t₂", "t₃"])
|
R, gens = polynomial_ring(Generic.Rationals{BigInt}(), ["x", "t₁", "t₂", "t₃"])
|
||||||
x = gens[1]
|
x = gens[1]
|
||||||
t = gens[2:4]
|
t = gens[2:4]
|
||||||
|
|
||||||
S, u = polynomial_ring(AbstractAlgebra.Rationals{BigInt}(), "u")
|
S, u = polynomial_ring(Generic.Rationals{BigInt}(), "u")
|
||||||
|
|
||||||
M = matrix_space(R, 7, 7)
|
M = matrix_space(R, 7, 7)
|
||||||
gram_symb = M(R[
|
gram_symb = M(R[
|
||||||
|
|||||||
@ -11,7 +11,7 @@ function printbad(msg)
|
|||||||
println(" ", msg)
|
println(" ", msg)
|
||||||
end
|
end
|
||||||
|
|
||||||
F, gens = rational_function_field(AbstractAlgebra.Rationals{BigInt}(), ["a₁", "a₂", "b₁", "b₂", "c₁", "c₂"])
|
F, gens = rational_function_field(Generic.Rationals{BigInt}(), ["a₁", "a₂", "b₁", "b₂", "c₁", "c₂"])
|
||||||
a = gens[1:2]
|
a = gens[1:2]
|
||||||
b = gens[3:4]
|
b = gens[3:4]
|
||||||
c = gens[5:6]
|
c = gens[5:6]
|
||||||
|
|||||||
@ -11,7 +11,7 @@ function printbad(msg)
|
|||||||
println(" ", msg)
|
println(" ", msg)
|
||||||
end
|
end
|
||||||
|
|
||||||
F, gens = rational_function_field(AbstractAlgebra.Rationals{BigInt}(), ["x", "t₁", "t₂", "t₃"])
|
F, gens = rational_function_field(Generic.Rationals{BigInt}(), ["x", "t₁", "t₂", "t₃"])
|
||||||
x = gens[1]
|
x = gens[1]
|
||||||
t = gens[2:4]
|
t = gens[2:4]
|
||||||
|
|
||||||
|
|||||||
Loading…
Reference in New Issue
Block a user